Question

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.

Answer 1

Foci (0, ±13), the conjugate axis is of length 24.
Here, the foci are on the y-axis.
Therefore, the equation of the hyperbola is of the form Y²/a² - x²/b² =1.
Since the foci are (0, ±13), c = 13.
Since the length of the conjugate axis is 24, 2b = 24 ⇒ b = 12.
We know that a² + b² = c².
∴a² + 12² = 13²
⇒ a² = 169 – 144 = 25
Thus, the equation of the hyperbola is Y²/25 - X²/144 =1.